Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 2 - Kinematics in One Dimension - Exercises and Problems - Page 66: 56

Answer

a) $ 1.96\;\rm h$ b) $72.86\;\rm mi$ c) See the graph below.

Work Step by Step

a) Ann will overtake Carol when they have the same position $x_f$. We know that both of them are moving at a constant speed but Carol's speed is greater than Ann's speed. $$x_{f,Carol}=x_{f,Ann}$$ $$ x_{i,Carol}+v_{Carol}\Delta t_{Carol}=\overbrace{x_{i,Ann} }^{0} +v_{Ann}\Delta t_{Ann}$$ $$x_{i,Carol} + v_{Carol}(t-0)= v_{Ann}(t-0.5)$$ Plugging the known and solving for $t$; $$2.4 +36t =50(t-0.5)=50t-25$$ $$50t-36t=2.4+25$$ Thus, $$t=\color{red}{\bf1.96}\;\rm h $$ b) Their position when Ann will overtake Carol is given by the position of any one of them since both will be at the same location. $$x_f=x_{f,Carol}=x_{i,Ann} +v_{Ann}\Delta t_{Ann}=2.4+36\cdot 1.96$$ $$x_{f }=\color{red}{\bf 72.86}\;\rm mi$$ c) Now we can draw the position-versus-time graph of both of them as you see below. Noting that Carol starts after Ann by an half hour. The blue line is for Carol and the magenta is for Ann.
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